Point Based
Rendering and Shadows

16 August 2001by
Forrester Cole

Point based rendering
is an alternative rendering technique to conventional polygon based
rendering. Instead of a set of triangles, the object is represented
by a cloud of single points, each with a surface normal. Point based
rendering is very useful for highly complex models, which would
otherwise require a huge number of triangles. It is also a natural
model for data captured by laser range scanners and similar devices,
which use a point cloud for their native representation. The session
included four papers, two of which are directly related to rendering
with points, and two that use point based techniques to enhance
polygon rendering.

The Randomized
z-Buffer Algorithm
The first paper presented a method of using point sampling to greatly
improve the efficiency of a conventional z-buffer, making it possible
to render extremely complex polygonal scenes at interactive rates.
The paper was the work of Michael Wand, Ingmar Peter, and Wolfgang
Strasser of the Universitaet Tuebingen, and Matthias Fischer and
Friedhelm Meyer auf der Heide of the Universitaet Paderborn. Wand
gave the presentation.

The algorithm
chooses which triangles to draw based on a random sample of points
collected in screen space. The authors were able to reduce the asymptotic
time taken to render extremely large polygon scenes from linear
to logarithmic. In a demonstration, Wand was able to render a scene
containing 10^14 triangles in only 40ms. Since the algorithm is
randomized, however, sparkling and other temporal artifacts can
be a problem. The authors tried to address the problem by averaging
images over several frames, but some demos still showed significant
sparkling in the distance.

Surface Splatting
Matthias Zwicker of Eidgenoessiche Technische Hochschule (ETH) Zuerich
presented the next paper, which directly tackled point based rendering.
The paper was co-authored by Markus Gross of ETH Zuerich, and Hanspeter
Pfister and Jeroen van Baar of Mitsubishi Electric Research Laboratory.
The algorithm addresses aliasing, a central problem of point based
rendering. To make a good image out of points, a reconstruction
filter must be used to blend over the holes between points. A naïve
filtering solution creates bad aliasing on distant points, where
more than one point may overlap in a single pixel.

The solution presented
by the authors uses a hybrid filter that both removes aliasing in
far points and blends near points without losing detail.

Spectral Processing
of Point-Sampled Geometry
The Fourier Transform is an indispensable tool for filtering and
spectral analysis on two dimensional signals, but it is tricky to
apply to irregularly sampled points on a 3D surface. The third paper,
authored by Mark Pauly and Markus Gross of ETH Zuerich, attempts
to adapt the Fourier Transform to a point-sampled manifold. The
goals of the work were to develop a method for spectral analysis
that allowed simple filtering but also maintained some local control
over that filtering. The Fourier Transform is a global operation,
and does not provide for any breakdown of a signal into local pieces.
Moreover, the Fast Fourier Transform algorithm requires a regularly
sampled grid, which a point cloud is decidedly not.

The solution that
the authors developed was to break the point cloud into a series
of patches, each of which could be transformed and manipulated independently.
Each patch is also resampled into a regular grid before transforming.
Any filtering operations can then be done easily in the frequency
domain. Another resampling step and recombination of the patches
yields the new, filtered point cloud. This system allows for good
local control and good filtering opportunities. An audience member
asked whether breaking the point cloud into patches introduced aliasing.
Pauly admitted that in theory it did, but in practice the effect
was not noticeable.

Adaptive Shadow
Maps
The final paper was not directly related to point based rendering,
but addressed the tangential problem of aliasing in shadow maps
from over-sampling. The paper was presented by Randima Fernando,
who authored it along with Sebastien Fernandez, Kavita Bala, and
Donald P. Greenberg, all from Cornell. Shadow maps are created at
a set resolution, which causes them to create pronounced jaggy artifacts
when their resolution is too low. To reduce these artifacts, programmers
are forced to spend large amounts of time optimizing the resolution
of shadow maps for appearance versus memory use. The new algorithm
simulates shadow maps of extremely high resolution by adaptively
increasing detail in the areas that need it most: the edges of shadows.
The algorithm can run at interactive rates on a PC, and uses a fixed
amount of memory no matter how close the camera zooms in on a shadow.
The tradeoff of the method comes in two parts. First, the algorithm
is much more complicated than conventional shadow mapping, and thus
is much slower. Even with optimization, calculating the change in
the hierarchical map takes time. Secondly, the method as presented
cannot take advantage of shadow mapping hardware currently available.